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UHE cosmic rays are thought to come from extra-galactic sources since galactic magnetic fields are too low to contain cosmic rays of this energy for very long and because the arrival directions are nearly isotropic. Cosmic rays propagating of cosmological distances are subject to various energy-loss effects, so that the energy we observe for a cosmic ray at earth may be quite different that the energy it was created with. Modeling what the observed spectrum should look like given an input spectrum involves extensive Monte Carlo modeling.